Multichannel Blind Deconvolution

We assume a standard acquisition model. The original image undergoes two degradations during the measurement: blurring and corruption by noise. The blur may be caused by several external effects, such as, atmospheric turbulence, camera lens, relative camera-scene motion, etc. Yet we will assume that we can model them as convolution with an unknown point spread function (PSF).

We have P blurred and noisy images zk and the goal of blind deconvolution is to estimate the original image u without any knowledge of blur kernels hk.

Multichannel blind deconvolution approaches required perfectly registered images. We have proofed that the inaccurate registration of images can be alleviated by properly overestimating a blur size adn we have proposed a novel blind deconvolution algorithm that can deal with the overestimated blur size. Alternating minimization (AM) scheme is used to find a maximum a posteriori (MAP) estimator.

The example below shows restoration of two real photos blurred by camera motion. On the left are two input images and on the right is the MAP estimator and reconstructed PSFs. The size of PSFs was set to (15x15).

Blind deconvolution of sunspot images

A sequence of short-exposure images of a sunspot was acquired with a terrestrial telescope. The images were taken shortly one after another and hence the image alignment was more or less assured and no registration was necessary. Atmospheric turbulence is the main cause of the image degradation but through its temporal fluctuations also provides the necessary co-primeness of channels. The least degraded image from the sequence, which is shown at the bottom right, was selected as a reference image. Two other images of median degradation (top row) were used as the input for the algorithm. The size of blurs was set to (12x12) which we believe to be large enough to contain the original blurs. The estimated original image at the bottom left was obtained after 3 iterations of AM.